Solve for x sec((3x)/2)=-2

Solve for x sec((3x)/2)=-2
Take the inverse secant of both sides of the equation to extract from inside the secant.
The exact value of is .
Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply .
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Multiply and .
Multiply by .
Multiply by .
The secant function is negative in the second and third quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.
Simplify the expression to find the second solution.
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Multiply both sides of the equation by .
Simplify both sides of the equation.
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Simplify the left side.
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Cancel the common factor of .
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Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
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Factor out of .
Cancel the common factor.
Rewrite the expression.
Simplify .
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To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by .
Combine the numerators over the common denominator.
Simplify the numerator.
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Multiply by .
Subtract from .
Multiply .
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Multiply and .
Multiply by .
Multiply by .
Find the period.
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The period of the function can be calculated using .
Replace with in the formula for period.
Solve the equation.
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is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply .
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Combine and .
Multiply by .
Combine and .
The period of the function is so values will repeat every radians in both directions.
, for any integer
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Name

Name three hundred two million fifty-two thousand one hundred eighty-two

Interesting facts

  • 302052182 has 8 divisors, whose sum is 454508496
  • The reverse of 302052182 is 281250203
  • Previous prime number is 317

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 23
  • Digital Root 5

Name

Name three hundred eighty-five million nine hundred eight thousand five hundred seventy-six

Interesting facts

  • 385908576 has 256 divisors, whose sum is 3911223024
  • The reverse of 385908576 is 675809583
  • Previous prime number is 1993

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 9
  • Sum of Digits 51
  • Digital Root 6

Name

Name one billion four hundred eighteen million nine hundred fifty-two thousand seven hundred ninety-six

Interesting facts

  • 1418952796 has 8 divisors, whose sum is 3192643800
  • The reverse of 1418952796 is 6972598141
  • Previous prime number is 2

Basic properties

  • Is Prime? no
  • Number parity even
  • Number length 10
  • Sum of Digits 52
  • Digital Root 7